On the homogenization of some free boundary problems.

Abstract: Free boundary problems arise in the modeling of many natural phenomena such as the combustion of a premixed gas or the shaping of capillary drops. Mathematically, these problems are known to yield very challenging questions. In this talk, I will discuss the effects of homogenization on the free boundary condition. In particular, I will show that oscillations arising along the free boundary typically yield hysteresis phenomena.